Geodesic
Lattices of subclasses.~III
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 252-263

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We prove that for certain $Q$-universal quasivarieties $\mathbf{K}$, the lattice of $\mathbf{K}$-quasivarieties contains continuum many subquasivarieties with the undecidable quasi-equational theory and for which the finite membership problem is also undecidable. Moreover, we prove that certain $Q$-universal quasivarieties have continuum many subquasivarieties with no independent quasi-equational basis.
Keywords: Abelian group, differential groupoid, finite membership problem, graph, independent basis, quasi-identity, quasi-equational theory, quasivariety, $Q$-universal, undecidable theory. 
@article{SEMR_2017_14_a7,
     author = {A. Basheyeva and A. Nurakunov and M. Schwidefsky and A. Zamojska-Dzienio},
     title = {Lattices of {subclasses.~III}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {252--263},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a7/}
}
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A. Basheyeva; A. Nurakunov; M. Schwidefsky; A. Zamojska-Dzienio. Lattices of subclasses.~III. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 252-263. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a7/